TSTP Solution File: LCL394-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LCL394-1 : TPTP v8.1.2. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 06:53:51 EDT 2023
% Result : Unsatisfiable 3.95s 3.97s
% Output : CNFRefutation 3.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 12
% Syntax : Number of formulae : 126 ( 41 unt; 7 typ; 0 def)
% Number of atoms : 218 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 204 ( 105 ~; 99 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 3 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-1 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 298 ( 77 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
implies: ( $i * $i ) > $i ).
tff(decl_23,type,
is_a_theorem: $i > $o ).
tff(decl_24,type,
not: $i > $i ).
tff(decl_25,type,
x: $i ).
tff(decl_26,type,
y: $i ).
tff(decl_27,type,
z: $i ).
tff(decl_28,type,
u: $i ).
cnf(condensed_detachment,axiom,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
cnf(cn_1,axiom,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_1) ).
cnf(cn_2,axiom,
is_a_theorem(implies(implies(not(X1),X1),X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_2) ).
cnf(cn_3,axiom,
is_a_theorem(implies(X1,implies(not(X1),X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_3) ).
cnf(prove_cn_58,negated_conjecture,
~ is_a_theorem(implies(implies(implies(implies(x,y),implies(implies(y,z),z)),u),implies(implies(not(x),z),u))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_58) ).
cnf(c_0_5,axiom,
( is_a_theorem(X2)
| ~ is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X1) ),
condensed_detachment ).
cnf(c_0_6,axiom,
is_a_theorem(implies(implies(X1,X2),implies(implies(X2,X3),implies(X1,X3)))),
cn_1 ).
cnf(c_0_7,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X3,X2))
| ~ is_a_theorem(implies(X1,X3)) ),
inference(spm,[status(thm)],[c_0_5,c_0_7]) ).
cnf(c_0_9,axiom,
is_a_theorem(implies(implies(not(X1),X1),X1)),
cn_2 ).
cnf(c_0_10,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X1,implies(X4,X3)))
| ~ is_a_theorem(implies(X2,X4)) ),
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_11,axiom,
is_a_theorem(implies(X1,implies(not(X1),X2))),
cn_3 ).
cnf(c_0_12,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(not(X2),X2))) ),
inference(spm,[status(thm)],[c_0_8,c_0_9]) ).
cnf(c_0_13,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X2,not(X1))) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_14,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(not(X2),not(X1))) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_5,c_0_11]) ).
cnf(c_0_16,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_17,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X2,X4))
| ~ is_a_theorem(implies(X4,X3)) ),
inference(spm,[status(thm)],[c_0_10,c_0_16]) ).
cnf(c_0_18,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(spm,[status(thm)],[c_0_5,c_0_9]) ).
cnf(c_0_19,plain,
( is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,X3))))
| ~ is_a_theorem(implies(X1,implies(X4,X2))) ),
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_20,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(X4,X3))
| ~ is_a_theorem(X4) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_21,plain,
is_a_theorem(implies(X1,X1)),
inference(spm,[status(thm)],[c_0_12,c_0_11]) ).
cnf(c_0_22,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(not(implies(implies(X1,X2),implies(X3,X2))),implies(X3,X1))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,plain,
( is_a_theorem(implies(X1,implies(not(X2),X3)))
| ~ is_a_theorem(implies(X1,X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_11]) ).
cnf(c_0_26,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_12,c_0_24]) ).
cnf(c_0_27,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_5,c_0_25]) ).
cnf(c_0_28,plain,
( is_a_theorem(implies(X1,implies(not(X2),X3)))
| ~ is_a_theorem(implies(X1,X4))
| ~ is_a_theorem(implies(X4,X2)) ),
inference(spm,[status(thm)],[c_0_8,c_0_25]) ).
cnf(c_0_29,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X3,X2)))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_8,c_0_26]) ).
cnf(c_0_30,plain,
( is_a_theorem(implies(not(implies(X1,X2)),X3))
| ~ is_a_theorem(implies(X4,X2))
| ~ is_a_theorem(implies(X1,X4)) ),
inference(spm,[status(thm)],[c_0_27,c_0_7]) ).
cnf(c_0_31,plain,
( is_a_theorem(implies(X1,implies(not(X2),X3)))
| ~ is_a_theorem(implies(implies(not(X1),X4),X2)) ),
inference(spm,[status(thm)],[c_0_28,c_0_11]) ).
cnf(c_0_32,plain,
is_a_theorem(implies(implies(not(implies(not(X1),X1)),implies(not(X1),X1)),X1)),
inference(spm,[status(thm)],[c_0_12,c_0_9]) ).
cnf(c_0_33,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_7]) ).
cnf(c_0_34,plain,
( is_a_theorem(implies(not(implies(X1,X2)),X3))
| ~ is_a_theorem(implies(X1,implies(not(X2),X2))) ),
inference(spm,[status(thm)],[c_0_30,c_0_9]) ).
cnf(c_0_35,plain,
is_a_theorem(implies(implies(not(X1),X1),implies(not(X1),X2))),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_9]) ).
cnf(c_0_37,plain,
is_a_theorem(implies(not(implies(implies(not(X1),X1),X1)),X2)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
is_a_theorem(implies(X1,implies(not(implies(not(X1),X2)),X3))),
inference(spm,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_39,plain,
( is_a_theorem(implies(implies(X1,X2),implies(not(X3),X4)))
| ~ is_a_theorem(implies(implies(implies(X2,X5),implies(X1,X5)),X3)) ),
inference(spm,[status(thm)],[c_0_28,c_0_6]) ).
cnf(c_0_40,plain,
is_a_theorem(implies(implies(implies(implies(not(X1),X1),X1),X2),X2)),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,plain,
is_a_theorem(implies(not(implies(X1,implies(not(X1),X2))),X3)),
inference(spm,[status(thm)],[c_0_34,c_0_38]) ).
cnf(c_0_42,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(not(implies(X1,X2)),X3))),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_43,plain,
is_a_theorem(implies(X1,implies(X2,implies(not(X2),X3)))),
inference(spm,[status(thm)],[c_0_14,c_0_41]) ).
cnf(c_0_44,plain,
is_a_theorem(implies(implies(X1,implies(not(X2),X2)),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_12,c_0_42]) ).
cnf(c_0_45,plain,
is_a_theorem(implies(implies(implies(not(X1),X2),X3),implies(X1,X3))),
inference(spm,[status(thm)],[c_0_22,c_0_43]) ).
cnf(c_0_46,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(not(implies(implies(X2,X1),X1)),X3))),
inference(spm,[status(thm)],[c_0_39,c_0_44]) ).
cnf(c_0_47,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(not(X1),X3),X2)) ),
inference(spm,[status(thm)],[c_0_5,c_0_45]) ).
cnf(c_0_48,plain,
is_a_theorem(implies(implies(not(X1),X2),implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_12,c_0_46]) ).
cnf(c_0_49,plain,
( is_a_theorem(implies(not(implies(implies(X1,X2),implies(X3,X2))),X4))
| ~ is_a_theorem(implies(X3,X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_6]) ).
cnf(c_0_50,plain,
is_a_theorem(implies(X1,implies(implies(X2,X1),X1))),
inference(spm,[status(thm)],[c_0_47,c_0_48]) ).
cnf(c_0_51,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_9]) ).
cnf(c_0_52,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(implies(not(X3),X3)) ),
inference(spm,[status(thm)],[c_0_20,c_0_9]) ).
cnf(c_0_53,plain,
( is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,X3))))
| ~ is_a_theorem(implies(X4,X2)) ),
inference(spm,[status(thm)],[c_0_14,c_0_49]) ).
cnf(c_0_54,plain,
( is_a_theorem(implies(X1,implies(X2,X1)))
| ~ is_a_theorem(implies(X2,implies(X3,X1))) ),
inference(spm,[status(thm)],[c_0_10,c_0_50]) ).
cnf(c_0_55,plain,
( is_a_theorem(implies(not(implies(X1,X2)),X3))
| ~ is_a_theorem(implies(not(X2),X2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_52]) ).
cnf(c_0_56,plain,
( is_a_theorem(implies(not(implies(X1,X2)),X3))
| ~ is_a_theorem(implies(not(X2),not(X1))) ),
inference(spm,[status(thm)],[c_0_34,c_0_13]) ).
cnf(c_0_57,plain,
( is_a_theorem(implies(X1,implies(X2,implies(X3,X4))))
| ~ is_a_theorem(implies(X2,implies(X5,X4)))
| ~ is_a_theorem(implies(X3,X5)) ),
inference(spm,[status(thm)],[c_0_10,c_0_53]) ).
cnf(c_0_58,plain,
is_a_theorem(implies(X1,implies(X2,X1))),
inference(spm,[status(thm)],[c_0_54,c_0_11]) ).
cnf(c_0_59,plain,
( is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(implies(not(implies(not(X1),X2)),X1)) ),
inference(spm,[status(thm)],[c_0_18,c_0_25]) ).
cnf(c_0_60,plain,
( is_a_theorem(implies(not(implies(X1,implies(X2,X3))),X4))
| ~ is_a_theorem(implies(not(X3),not(X2))) ),
inference(spm,[status(thm)],[c_0_55,c_0_56]) ).
cnf(c_0_61,plain,
( is_a_theorem(implies(X1,implies(X2,implies(X3,X2))))
| ~ is_a_theorem(implies(X3,X4)) ),
inference(spm,[status(thm)],[c_0_57,c_0_58]) ).
cnf(c_0_62,plain,
( is_a_theorem(implies(not(X1),implies(X2,X3)))
| ~ is_a_theorem(implies(not(X3),not(X2))) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_63,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X2)))),
inference(spm,[status(thm)],[c_0_61,c_0_11]) ).
cnf(c_0_64,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(not(implies(not(X2),X2)),implies(not(X2),X2)))) ),
inference(spm,[status(thm)],[c_0_8,c_0_32]) ).
cnf(c_0_65,plain,
is_a_theorem(implies(implies(X1,not(X2)),implies(not(implies(X2,implies(X1,X3))),X4))),
inference(spm,[status(thm)],[c_0_39,c_0_45]) ).
cnf(c_0_66,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(implies(not(X1),not(X3))) ),
inference(spm,[status(thm)],[c_0_22,c_0_62]) ).
cnf(c_0_67,plain,
is_a_theorem(implies(implies(implies(X1,X2),X3),implies(X2,X3))),
inference(spm,[status(thm)],[c_0_22,c_0_63]) ).
cnf(c_0_68,plain,
is_a_theorem(implies(implies(X1,not(not(implies(X1,X2)))),implies(X1,X2))),
inference(spm,[status(thm)],[c_0_64,c_0_65]) ).
cnf(c_0_69,plain,
( is_a_theorem(implies(X1,implies(not(implies(X2,X3)),X4)))
| ~ is_a_theorem(implies(not(not(X1)),not(X2))) ),
inference(spm,[status(thm)],[c_0_31,c_0_66]) ).
cnf(c_0_70,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(implies(X3,X1),X2)) ),
inference(spm,[status(thm)],[c_0_5,c_0_67]) ).
cnf(c_0_71,plain,
( is_a_theorem(implies(implies(X1,not(not(implies(X1,X2)))),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_29,c_0_68]) ).
cnf(c_0_72,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(not(X1)) ),
inference(spm,[status(thm)],[c_0_14,c_0_16]) ).
cnf(c_0_73,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(not(not(X1)),not(not(X2)))) ),
inference(spm,[status(thm)],[c_0_64,c_0_69]) ).
cnf(c_0_74,plain,
( is_a_theorem(implies(not(not(implies(X1,X2))),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_70,c_0_71]) ).
cnf(c_0_75,plain,
( is_a_theorem(implies(X1,implies(X2,X3)))
| ~ is_a_theorem(not(not(X3))) ),
inference(spm,[status(thm)],[c_0_52,c_0_72]) ).
cnf(c_0_76,plain,
( is_a_theorem(implies(implies(X1,not(not(X2))),X2))
| ~ is_a_theorem(X1) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_77,plain,
is_a_theorem(implies(implies(X1,not(X2)),implies(X2,implies(X1,X3)))),
inference(spm,[status(thm)],[c_0_12,c_0_65]) ).
cnf(c_0_78,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X2)))
| ~ is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_22,c_0_75]) ).
cnf(c_0_79,plain,
( is_a_theorem(implies(not(not(X1)),X1))
| ~ is_a_theorem(X2) ),
inference(spm,[status(thm)],[c_0_70,c_0_76]) ).
cnf(c_0_80,plain,
is_a_theorem(implies(not(X1),implies(X1,implies(X2,X3)))),
inference(spm,[status(thm)],[c_0_70,c_0_77]) ).
cnf(c_0_81,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(implies(not(X2),X1)) ),
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_82,plain,
( is_a_theorem(implies(implies(X1,X2),X2))
| ~ is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_12,c_0_78]) ).
cnf(c_0_83,plain,
is_a_theorem(implies(not(not(X1)),X1)),
inference(spm,[status(thm)],[c_0_79,c_0_80]) ).
cnf(c_0_84,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X1),X2))
| ~ is_a_theorem(implies(X2,X1)) ),
inference(spm,[status(thm)],[c_0_5,c_0_81]) ).
cnf(c_0_85,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X3,X2)))
| ~ is_a_theorem(not(not(X3))) ),
inference(spm,[status(thm)],[c_0_8,c_0_82]) ).
cnf(c_0_86,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(not(X2),X2)) ),
inference(spm,[status(thm)],[c_0_14,c_0_51]) ).
cnf(c_0_87,plain,
is_a_theorem(implies(X1,not(not(X1)))),
inference(spm,[status(thm)],[c_0_14,c_0_83]) ).
cnf(c_0_88,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(implies(not(X2),X3),X1))
| ~ is_a_theorem(implies(not(X1),X2)) ),
inference(spm,[status(thm)],[c_0_84,c_0_25]) ).
cnf(c_0_89,plain,
( is_a_theorem(implies(implies(not(implies(X1,X2)),implies(X1,X2)),X2))
| ~ is_a_theorem(not(not(X1))) ),
inference(spm,[status(thm)],[c_0_85,c_0_9]) ).
cnf(c_0_90,plain,
( is_a_theorem(implies(X1,implies(implies(X2,X3),implies(X4,X3))))
| ~ is_a_theorem(implies(not(implies(implies(X2,X3),implies(X4,X3))),implies(X4,X2))) ),
inference(spm,[status(thm)],[c_0_86,c_0_19]) ).
cnf(c_0_91,plain,
is_a_theorem(implies(X1,implies(implies(not(X2),X2),X2))),
inference(spm,[status(thm)],[c_0_14,c_0_37]) ).
cnf(c_0_92,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,not(X3)))
| ~ is_a_theorem(implies(not(X3),X3)) ),
inference(spm,[status(thm)],[c_0_8,c_0_51]) ).
cnf(c_0_93,plain,
is_a_theorem(implies(X1,not(not(implies(X2,X1))))),
inference(spm,[status(thm)],[c_0_70,c_0_87]) ).
cnf(c_0_94,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X1),implies(X2,X1)))
| ~ is_a_theorem(not(not(X2))) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_95,plain,
is_a_theorem(implies(X1,implies(implies(X2,X3),implies(implies(not(X2),X2),X3)))),
inference(spm,[status(thm)],[c_0_90,c_0_91]) ).
cnf(c_0_96,plain,
( is_a_theorem(implies(implies(not(not(X1)),not(X1)),X2))
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(spm,[status(thm)],[c_0_92,c_0_9]) ).
cnf(c_0_97,negated_conjecture,
~ is_a_theorem(implies(implies(implies(implies(x,y),implies(implies(y,z),z)),u),implies(implies(not(x),z),u))),
prove_cn_58 ).
cnf(c_0_98,plain,
( is_a_theorem(implies(X1,X2))
| ~ is_a_theorem(implies(X1,implies(X3,X2)))
| ~ is_a_theorem(implies(not(X2),X3)) ),
inference(spm,[status(thm)],[c_0_8,c_0_81]) ).
cnf(c_0_99,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X1,X3)))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_29,c_0_6]) ).
cnf(c_0_100,plain,
is_a_theorem(implies(not(implies(X1,not(X2))),X2)),
inference(spm,[status(thm)],[c_0_14,c_0_93]) ).
cnf(c_0_101,plain,
( is_a_theorem(implies(implies(not(X1),X1),X2))
| ~ is_a_theorem(not(not(implies(X1,X2)))) ),
inference(spm,[status(thm)],[c_0_94,c_0_95]) ).
cnf(c_0_102,plain,
( is_a_theorem(X1)
| ~ is_a_theorem(implies(not(X1),not(X2)))
| ~ is_a_theorem(implies(not(X2),X2)) ),
inference(spm,[status(thm)],[c_0_88,c_0_96]) ).
cnf(c_0_103,plain,
is_a_theorem(implies(X1,implies(implies(X1,X2),X2))),
inference(spm,[status(thm)],[c_0_70,c_0_48]) ).
cnf(c_0_104,negated_conjecture,
~ is_a_theorem(implies(implies(not(x),z),implies(implies(x,y),implies(implies(y,z),z)))),
inference(spm,[status(thm)],[c_0_97,c_0_7]) ).
cnf(c_0_105,plain,
( is_a_theorem(implies(implies(X1,X2),X3))
| ~ is_a_theorem(implies(not(X3),X1))
| ~ is_a_theorem(implies(X2,X3)) ),
inference(spm,[status(thm)],[c_0_98,c_0_99]) ).
cnf(c_0_106,plain,
( is_a_theorem(implies(X1,not(X2)))
| ~ is_a_theorem(implies(X2,implies(X1,not(X2)))) ),
inference(spm,[status(thm)],[c_0_84,c_0_100]) ).
cnf(c_0_107,plain,
( is_a_theorem(implies(X1,implies(not(X2),X3)))
| ~ is_a_theorem(not(not(implies(X1,X2)))) ),
inference(spm,[status(thm)],[c_0_31,c_0_101]) ).
cnf(c_0_108,plain,
( is_a_theorem(not(not(X1)))
| ~ is_a_theorem(implies(not(X1),X1)) ),
inference(spm,[status(thm)],[c_0_102,c_0_83]) ).
cnf(c_0_109,plain,
( is_a_theorem(implies(X1,implies(X2,implies(X3,X4))))
| ~ is_a_theorem(implies(X3,implies(X2,X4))) ),
inference(spm,[status(thm)],[c_0_57,c_0_103]) ).
cnf(c_0_110,negated_conjecture,
( ~ is_a_theorem(implies(not(implies(implies(x,y),implies(implies(y,z),z))),not(x)))
| ~ is_a_theorem(implies(z,implies(implies(x,y),implies(implies(y,z),z)))) ),
inference(spm,[status(thm)],[c_0_104,c_0_105]) ).
cnf(c_0_111,plain,
is_a_theorem(implies(X1,implies(X2,implies(X3,X1)))),
inference(spm,[status(thm)],[c_0_70,c_0_58]) ).
cnf(c_0_112,plain,
( is_a_theorem(implies(not(X1),not(X2)))
| ~ is_a_theorem(not(not(implies(X2,X1)))) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_113,plain,
( is_a_theorem(not(not(implies(X1,implies(X2,X3)))))
| ~ is_a_theorem(implies(X2,implies(X1,X3))) ),
inference(spm,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_114,negated_conjecture,
~ is_a_theorem(implies(not(implies(implies(x,y),implies(implies(y,z),z))),not(x))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_110,c_0_111])]) ).
cnf(c_0_115,plain,
( is_a_theorem(implies(not(implies(X1,X2)),not(X3)))
| ~ is_a_theorem(implies(X1,implies(X3,X2))) ),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_116,negated_conjecture,
~ is_a_theorem(implies(implies(x,y),implies(x,implies(implies(y,z),z)))),
inference(spm,[status(thm)],[c_0_114,c_0_115]) ).
cnf(c_0_117,plain,
( is_a_theorem(implies(implies(X1,X2),implies(X3,X4)))
| ~ is_a_theorem(implies(X3,X1))
| ~ is_a_theorem(implies(X2,X4)) ),
inference(spm,[status(thm)],[c_0_10,c_0_99]) ).
cnf(c_0_118,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_117]),c_0_21]),c_0_103])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : LCL394-1 : TPTP v8.1.2. Released v2.3.0.
% 0.12/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Aug 24 17:17:06 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.58 start to proof: theBenchmark
% 3.95/3.96 % Version : CSE_E---1.5
% 3.95/3.96 % Problem : theBenchmark.p
% 3.95/3.97 % Proof found
% 3.95/3.97 % SZS status Theorem for theBenchmark.p
% 3.95/3.97 % SZS output start Proof
% See solution above
% 3.95/3.97 % Total time : 3.375000 s
% 3.95/3.97 % SZS output end Proof
% 3.95/3.97 % Total time : 3.378000 s
%------------------------------------------------------------------------------